Montreal Geometric & Combinatorial Group Theory Seminar
Speaker: John Meier (Lafayette & Columbia)
Title: “Asymptotic cohomology of the group of loops”
Date: 3:30PM, Monday, September 29, 2003
Place: Room 1120, Burnside Hall, McGill University
Let L_n denote n unknotted, unlinked circles in S^3. Much as one can describe the n-strand braid group as the motion group of n points in a disk, one can define the motion group of L_n in S^3: elements consist of finite length movies where the n circles are allowed to fly about in the 3-sphere, never intersecting, and returning to their original configuration at the end of the film. This talk will focus on work with Jon McCammond, where we compute the L^2 cohomology of this group. The argument eventually boils down to doing some enumerative combinatorics on a poset of hypertrees.